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Simplify the expression. Write your answers using integers or improper fractions. 4(5x-2x-4)+(1)/(2)x Answer:

Simplify the expression. Write your answers using integers or improper fractions.\newline4(5x−2x−4)+12x 4(5 x-2 x-4)+\frac{1}{2} x \newlineAnswer:

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Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.\newline4(5x−2x−4)+12x 4(5 x-2 x-4)+\frac{1}{2} x \newlineAnswer:
  1. Distribute Terms: Distribute 44 into the terms inside the parentheses (5x−2x−4)(5x-2x-4). \newline4×5x=20x4 \times 5x = 20x\newline4×(−2x)=−8x4 \times (-2x) = -8x\newline4×(−4)=−164 \times (-4) = -16
  2. Combine Distributed Terms: Combine the distributed terms. 20x−8x−1620x - 8x - 16
  3. Simplify Expression: Simplify the expression by combining like terms 20x20x and −8x-8x.20x−8x=12x20x - 8x = 12xSo, we have 12x−1612x - 16.
  4. Add Term: Add the term (12)x(\frac{1}{2})x to the simplified expression from Step 33.\newline12x−16+(12)x12x - 16 + (\frac{1}{2})x
  5. Find Common Denominator: Find a common denominator to combine the terms 12x12x and (1/2)x(1/2)x. The common denominator is 22. We can write 12x12x as (24/2)x(24/2)x. (24/2)x+(1/2)x(24/2)x + (1/2)x
  6. Combine Like Terms: Combine the like terms (242)x(\frac{24}{2})x and (12)x(\frac{1}{2})x.242x+12x=252x\frac{24}{2}x + \frac{1}{2}x = \frac{25}{2}x
  7. Write Final Expression: Write the final simplified expression.\newlineThe final expression is (252)x−16(\frac{25}{2})x - 16.

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